Calculation of the criteria deviator and the vector of normal to the deviator section of the yield surface for the Murnaghan elastic-plastic material 1

Abstract

For the generalized elastic-plastic material of Murnaghan the software implementation procedures were obtained and a set of programs was developed to calculate the criterion deviator and the external normal vector to the surface of the deviator section of the yield surface. The criterion deviator is decomposed into the sum of three deviators as isotropic, anisotropy and the vortex. Anisotropy deviator is formed from anisotropic structures of the second and third degrees of the specific potential energy of elastic deformation. The transition from material indifferent quantities into the expansion to invariant quantities is made by orthogonal transformation with the orthogonal elastic rotation tensor itself. The necessary analytical relations were obtained for calculating the transformed criteria deviator as a symmetric operator in the five-dimensional vector space of stress deviators. The vectors of external normal for the singular point of the yield surface in the space of stress deviators are determined by two eigenvectors of the operator, and for a regular point by one of them. The calculation of quantities sought is carried out for the elastic type of Murnaghan material of general form – triclinic.